NCRT Maths 10th 2.2therom
Answers
Answer:
Step-by-step explanation:
Similarity Criteria
All congruent figures are similar, but it does not mean that all similar figures are congruent.
Two polygons of the same number of sides are similar, if:
Their corresponding angles are equal.
Their corresponding sides are in the same ratio.
Two triangles are similar, if:
Their corresponding angles are equal.
Their corresponding sides are in the same ratio.
OR
The inverse of a real number a is denoted by a
−1
. For example,
7
−1 = 1/7 and
7 · 7
−1 = 7−1
· 7 = 1.
The Inverse of a Matrix
An n × n matrix A is said to be invertible if there is an n × n
matrix C satisfying
CA = AC = In
where In is the n × n identity matrix. We call C the inverse of A .
Jiwen He, University of Houston Math 2331, Linear Algebra 3 / 16
2.2 The Inverse of a Matrix Definition Solution Elementary Matrix
The Inverse of a Matrix: Facts
Fact
If A is invertible, then the inverse is unique.
Proof: Assume B and C are both inverses of A. Then
B = BI = B ( ) = ( ) = I = C.
So the inverse is unique since any two inverses coincide.
Notation
The inverse of A is usually denoted by A
−1
.
We have
AA−1 = A
−1A = In
Not all n × n matrices are invertible. A matrix which is not
invertible is sometimes called a singular matrix. An invertible
matrix is called nonsingular matrix.
wHICH ONE IS FOR YOU TELL ME ND WHETHER CORRECT??